Hi David, welcome to PP. Just added some info about the bus situation here in Paphos.
Here's the link to the Bus timesheet/routes, if you've not already found it.
http://www.pafosbuses.com/I'm not a 100% sure, but I don't think there's a bus to the international school (or close). There may be a school bus - not sure.
The closest stop is the Anavargos/general hospital stop, which is quite a way at least 40mins walk. The last bus to/from there is 2pm - yes in the afternoon.
The buses are only useful if you live along the coast road or in the central Paphos town area and you want to get to somewhere in those sorts of areas or the airports.
If you can't drive or don't want a car and want to live in Cyprus you will have to use a taxi on fairly regular bases. With time may be get some sort of lift sharing system with neighbours/friends.